11,228 research outputs found
Can One Trust Quantum Simulators?
Various fundamental phenomena of strongly-correlated quantum systems such as
high- superconductivity, the fractional quantum-Hall effect, and quark
confinement are still awaiting a universally accepted explanation. The main
obstacle is the computational complexity of solving even the most simplified
theoretical models that are designed to capture the relevant quantum
correlations of the many-body system of interest. In his seminal 1982 paper
[Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models
might be solved by "simulation" with a new type of computer whose constituent
parts are effectively governed by a desired quantum many-body dynamics.
Measurements on this engineered machine, now known as a "quantum simulator,"
would reveal some unknown or difficult to compute properties of a model of
interest. We argue that a useful quantum simulator must satisfy four
conditions: relevance, controllability, reliability, and efficiency. We review
the current state of the art of digital and analog quantum simulators. Whereas
so far the majority of the focus, both theoretically and experimentally, has
been on controllability of relevant models, we emphasize here the need for a
careful analysis of reliability and efficiency in the presence of
imperfections. We discuss how disorder and noise can impact these conditions,
and illustrate our concerns with novel numerical simulations of a paradigmatic
example: a disordered quantum spin chain governed by the Ising model in a
transverse magnetic field. We find that disorder can decrease the reliability
of an analog quantum simulator of this model, although large errors in local
observables are introduced only for strong levels of disorder. We conclude that
the answer to the question "Can we trust quantum simulators?" is... to some
extent.Comment: 20 pages. Minor changes with respect to version 2 (some additional
explanations, added references...
Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
We compute the error threshold of color codes, a class of topological quantum
codes that allow a direct implementation of quantum Clifford gates, when both
qubit and measurement errors are present. By mapping the problem onto a
statistical-mechanical three-dimensional disordered Ising lattice gauge theory,
we estimate via large-scale Monte Carlo simulations that color codes are stable
against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson
loop distributions, we introduce a very sensitive probe to locate first-order
phase transitions in lattice gauge theories.Comment: 12 pages, 5 figures, 1 tabl
Simulating quantum mechanics on a quantum computer
Algorithms are described for efficiently simulating quantum mechanical
systems on quantum computers. A class of algorithms for simulating the
Schrodinger equation for interacting many-body systems are presented in some
detail. These algorithms would make it possible to simulate nonrelativistic
quantum systems on a quantum computer with an exponential speedup compared to
simulations on classical computers. Issues involved in simulating relativistic
systems of Dirac and gauge particles are discussed.Comment: 22 pages LaTeX; Expanded version of a talk given by WT at the
PhysComp '96 conference, BU, Boston MA, November 1996. Minor corrections
made, references adde
Generating and verifying graph states for fault-tolerant topological measurement-based quantum computing in 2D optical lattices
We propose two schemes for implementing graph states useful for
fault-tolerant topological measurement-based quantum computation in 2D optical
lattices. We show that bilayer cluster and surface code states can be created
by global single-row and controlled-Z operations. The schemes benefit from the
accessibility of atom addressing on 2D optical lattices and the existence of an
efficient verification protocol which allows us to ensure the experimental
feasibility of measuring the fidelity of the system against the ideal graph
state. The simulation results show potential for a physical realization toward
fault-tolerant measurement-based quantum computation against dephasing and
unitary phase errors in optical lattices.Comment: 6 pages and 4 figures (minor changed
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